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Identified errors:
This is not correct for Romania: officially it’s Surname + Given-name, live in Hungary.
Not true for Greece, it’s just First-name + Surname. It just happens that some Surnames are derived from the father’s name (think “Anderson”).
In Spain of course your parents have 2 surnames too. So your first surname is your father's first surname, his 2nd surname is dropped ( first surname of his mother ) Your second surname is the first surname of your mother, her 2nd gets dropped too.
In the end always the name line of the females get dropped.
Historically, yes; however, they passed a law some years ago to allow for the mother's surname to be the first surname, as it happens in Portugal. Nonetheless I am not sure how popular this is.